Editing Orthogonal complement (section)

==Applications==
In [[special relativity]] the orthogonal complement is used to determine the [[world line#Simultaneous hyperplane|simultaneous hyperplane]] at a point of a [[world line]]. The bilinear form <math>\eta</math> used in [[Minkowski space]] determines a [[pseudo-Euclidean space]] of events.<ref>[[G. D. Birkhoff]] (1923) ''Relativity and Modern Physics'', pages 62,63, [[Harvard University Press]]</ref> The origin and all events on the [[light cone]] are self-orthogonal. When a [[time]] event and a [[space]] event evaluate to zero under the bilinear form, then they are [[hyperbolic-orthogonal]]. This terminology stems from the use of [[conjugate hyperbola]]s in the pseudo-Euclidean plane: [[conjugate diameters]] of these hyperbolas are hyperbolic-orthogonal.